Question

A fraction becomes 4 when 1 is added to both the numerator and denominator and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is -

• A. $2$
• B. $3$
• C. $5$
• D. $15$

Answer 1

Answer: (D)

$15$

Let the fraction be $\frac{x}{y}$

Then according to the question,

$\frac{x+1}{y+1}=4$ .....(1) and $\frac{x-1}{y-1}=7$ .....(2)

From (1),

$x+1=4(y+1)$

$x=4y+3$ ....(3)

From (2),

$x-1=7(y-1)$

$x=7y-6$ ....(4)

From (3) and (4),

$4y+3=7y-6$

$3y=9$

$y=3$ ...(5)

From (4) and (5),

$x=4\times 3+3=15$

Numerator of the fraction =$x$=15